We start by sketching the triangle ABC as shown below. We label the side with the small letters a,b, and c on the opposite of the angle A, B, and C
The angle m<C is labeled x
To work out the size of x, we use the cosine rule
[tex]c^{2}= a^{2}+ b^{2}-2ab(cos(x)) [/tex]
[tex]6^{2}= 3.5^{2}+ 5.5^{2}-(2)(3.5)(5.5)(cos(x)) [/tex]
[tex]36=12.25+30.25-(38.5cos(x))[/tex]
[tex]36=42.5-38.5cos(x)[/tex]
[tex]36-42.5=-38.5cos(x)[/tex]
[tex]-6.5=-38.5cos(x)[/tex]
[tex]cos(x)= \frac{6.5}{38.5} [/tex]
[tex]x= cos^{-1}( \frac{6.5}{38.5})
[tex]x=80.3[/tex]5} )}[/tex] to one decimal place
